Monday marked the first day of trading for the region since the People's Bank of China on Friday said it would reduce the amount of cash banks have to keep in reserve, a move which could unleash 900 billion yuan ($126 billion) for long-term lending. The central bank has indicated that it could take more steps to stimulate the economy.

China's economy continues to show signs of weakness. Exports unexpectedly shrank by 1% last month, according to data released over the weekend. Analysts polled by Reuters expected those figures to rise.

Exports in August to the United States fell 16% compared to a year ago. The country has been locked in a trade war with the United States.

Elsewhere in the region, Japan revealed that its economy grew slower than what was estimated in the second quarter. The country revised its GDP growth to 1.3% for the quarter, compared to the 1.8% that was initially estimated, according to data published by the Cabinet Office.

Japan's central bank meets next week. Japan's interest rates are already very low, and investors are looking out to see whether the central bank will ease its monetary policy even further in the future.

"Traders are ... leaning on the pillars of support from monetary policymakers," wrote Stephen Innes, a market strategist for Asia Pacific at AxiTrader, in a report Monday. He added that expectations are high for central bankers to take steps to support their economies.

Investors are also looking ahead to the European Central Bank's policy decision on Thursday, Innes wrote.

The Federal Reserve, meanwhile, holds its September meeting next week. Chairman Jerome Powell on Friday repeated a pledge to do whatever it takes to keep the US economy growing — comments widely seen as a signal that policymakers could cut rates again.